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Matching (version 1.7)

Match: Multivariate and Propensity Score Matching Estimator for Causal Inference

Description

This function preforms multivariate matching. This function is intended to be used in conjunction with the MatchBalance function which checks if the results of this function have actually achieved balance on a set of covariates. If one wants to do propensity score matching, one should estimate the propensity model before calling Match, and then send Match the propensity scores to use. The GenMatch function can be used to automatically find balance by the use of a genetic search algorithm which determines the optimal weight to give each covariate. Match provides principled standard errors when matching is done with covariates or a known propensity score. Ties are handled in a deterministic and coherent fashion.

Usage

Match(Y=NULL, Tr, X, Z = X, V = rep(1, length(Y)), estimand = "ATT", M = 1,
      BiasAdjust = FALSE, exact = NULL, caliper = NULL,
      Weight = 1, Weight.matrix = NULL, weights = rep(1, length(Y)),
      Var.calc = 0, sample = FALSE, tolerance = 1e-05,
      distance.tolerance = 1e-05, restrict=NULL, version="fast")

Arguments

Y
A vector containing the outcome of interest. Missing values are not allowed. An outcome vector is not required because the matches generated will be the same regardless of the outcomes. Of course without any outcomes, no causal effect es
Tr
A vector indicating the observations which are in the treatment regime and those which are not. This can either be a logical vector or a real vector where 0 denotes control and 1 denotes treatment.
X
A matrix containing the variables we wish to match on. This matrix may contain the actual observed covariates or the propensity score or a combination of both. All columns of this matrix must have positive variance or Match will r
Z
A matrix containing the covariates for which we wish to make bias adjustments.
V
A matrix containing the covariates for which the variance of the causal effect may vary. Also see the Var.calc option, which takes precedence.
estimand
A character string for the estimand. The default estimand is "ATT", the sample average treatment effect for the treated. "ATE" is the sample average treatment effect (for all), and "ATC" is the sample average treatment effect for the controls
M
A scalar for the number of matches which should be found (with replacement). The default is one-to-one matching.
BiasAdjust
A logical scalar for whether regression adjustment should be used. See the Z matrix.
exact
A logical scalar or vector for whether exact matching should be done. Variables which are to be exactly matched on should also be given a very large weight (e.g., 1000) via the Weight.matrix option. If a logical scal
caliper
A scalar or vector denoting the caliper(s) which should be used when matching. Variables for which a caliper is to be used should also be given a very large weight (e.g., 1000) via the Weight.matrix option. A calipe
Weight
A scalar for the type of weighting scheme the matching algorithm should use when weighting each of the covariates in X. The default value of 1 denotes that weights are equal to the inverse of the variances. 2 denotes the Maha
Weight.matrix
This matrix denotes the weights the matching algorithm uses when weighting each of the covariates in X---see the Weight option. This square matrix should have as many columns as the number of columns of the X
weights
A vector the same length as Y which provides observations specific weights.
Var.calc
A scalar for the variance estimate that should be used. By default Var.calc=0 which means that homoscedasticity is assumed. For values of Var.calc > 0, robust variances are calculated using Var.calc ma
sample
A logical flag for whether the population or sample variance is returned.
tolerance
This is a scalar which is used to determine numerical tolerances. This option is used by numerical routines such as those used to determine if a matrix is singular.
distance.tolerance
This is a scalar which is used to determine if distances between two observations are different from zero. Values less than distance.tolerance are deemed to be equal to zero. This option can be used to perform a type of optimal
restrict
A matrix which restricts the possible matches. This matrix has one row for each restriction and three columns. The first two columns contain the two observation numbers which are to be restricted (for example 4 and 20), and the third col
version
The version of the code to be used. The "fast" C/C++ version of the code is used unless the "old" (stable) version is requested.

Value

  • estThe estimated average causal effect.
  • seThe standard error. This standard error is principled if X consists of either covariates or a known propensity score because it takes into account the uncertainty of the matching procedure. If an estimated propensity score is used, the uncertainty involved in its estimation is not accounted for although the uncertainty of the matching procedure itself still is.
  • est.noadjThe estimated average causal effect without any BiasAdjust. If BiasAdjust is not requested, this is the same as est.
  • se.naiveThe naive standard error. This is the standard error calculated on the matched data using the usual method of calculating the difference of means (between treated and control) weighted by the observation weights provided by weights. Note that the standard error provided by se takes into account the uncertainty of the matching procedure while se.naive does not. Neither se nor se.naive take into account the uncertainty of estimating a propensity score. se.naive does not take into account any BiasAdjust. Summary of the naive results can be requested by setting the full=TRUE flag when using the summary.Match function on the object returned by Match.
  • se.condThe conditional standard error. The practitioner should not generally use this.
  • mdataA list which contains the matched datasets produced by Match. Three datasets are included in this list: Y, Tr and X.
  • index.treatedA vector containing the observation numbers from the original dataset for the treated observations in the matched dataset. This index in conjunction with index.control can be used to recover the matched dataset produced by Match. For example, the X matrix used by Match can be recovered by rbind(X[index.treated,],X[index.control,]). The user should generally just examine the output of mdata.
  • index.controlAn index for the control observations in the matched data. This index in conjunction with index.treated can be used to recover the matched dataset produced by Match. For example, the X matrix used by Match can be recovered by rbind(X[index.treated,],X[index.control,]). The user should generally just examine the output of mdata.
  • weightsThe weight for the matched dataset. If all of the observations had a weight of 1 on input, they will have a weight of 1 on output if each observation was only matched once.
  • orig.nobsThe original number of observations in the dataset.
  • orig.wnobsThe original number of weighted observations in the dataset.
  • orig.treated.nobsThe original number of treated observations (unweighted).
  • nobsThe number of observations in the matched dataset.
  • wnobsThe number of weighted observations in the matched dataset.
  • caliperThe caliper which was used.
  • ecaliperThe size of the enforced caliper on the scale of the X variables. This object has the same length as the number of covariates in X.
  • exactThe value of the exact function argument.
  • ndropsThe number of actual observations which were dropped either because of caliper or exact matching. This number is not reliable if observation specific weights were passed in using the weights option. But ndrops.matches will always be accurate.
  • ndrops.matchesThe number of matches including ties which were dropped either because of the caliper or exact matching. Note that since this number includes ties, it is not the same as ndrops.

Details

This function is intended to be used in conjunction with the MatchBalance function which checks if the results of this function have actually achieved balance. The results of this function can be summarized by a call to the summary.Match function. If one wants to do propensity score matching, one should estimate the propensity model before calling Match, and then place the fitted values in the X matrix---see the provided example. The GenMatch function can be used to automatically find balance by the use of a genetic search algorithm which determines the optimal weight to give each covariate. The object returned by GenMatch can be supplied to the Weight.matrix option of Match to obtain estimates. Three demos are included: GerberGreenImai, DehejiaWahba, and AbadieImbens. These can be run by calling the demo function such as by demo(DehejiaWahba).

References

Abadie, Alberto and Guido Imbens. 2005. ``Large Sample Properties of Matching Estimators for Average Treatment Effects.'' Econometrica. http://ksghome.harvard.edu/~.aabadie.academic.ksg/sme.pdf

Diamond, Alexis and Jasjeet S. Sekhon. 2005. ``Genetic Matching for Estimating Causal Effects: A General Multivariate Matching Method for Achieving Balance in Observational Studies.'' Working Paper. http://sekhon.polisci.berkeley.edu/papers/GenMatch.pdf

Imbens, Guido. 2004. Matching Software for Matlab and Stata. http://elsa.berkeley.edu/~imbens/estimators.shtml Sekhon, Jasjeet S. 2004. ``The Varying Role of Voter Information Across Democratic Societies.'' Working Paper. http://sekhon.polisci.berkeley.edu/papers/SekhonInformation.pdf

See Also

Also see summary.Match, GenMatch, MatchBalance, balanceMV, balanceUV, ks.boot, GerberGreenImai, lalonde

Examples

Run this code
#
# Replication of Dehejia and Wahba psid3 model
#
# Dehejia, Rajeev and Sadek Wahba. 1999.``Causal Effects in Non-Experimental Studies: Re-Evaluating the
# Evaluation of Training Programs.''Journal of the American Statistical Association 94 (448): 1053-1062.
#
data(lalonde)

#
# Estimate the propensity model
#
glm1  <- glm(treat~age + I(age^2) + educ + I(educ^2) + black +
             hisp + married + nodegr + re74  + I(re74^2) + re75 + I(re75^2) +
             u74 + u75, family=binomial, data=lalonde)


#
#save data objects
#
X  <- glm1$fitted
Y  <- lalonde$re78
Tr  <- lalonde$treat

#
# one-to-one matching with replacement (the "M=1" option).
# Estimating the treatment effect on the treated (the "estimand" option which defaults to 0).
#
rr  <- Match(Y=Y,Tr=Tr,X=X,M=1);
summary(rr)

#
# Let's check for balance
# 'nboots' and 'nmc' are set to small values in the interest of speed.
# Please increase to at least 500 each for publication quality p-values.  
mb  <- MatchBalance(treat~age + I(age^2) + educ + I(educ^2) + black +
                    hisp + married + nodegr + re74  + I(re74^2) + re75 + I(re75^2) +
                    u74 + u75, data=lalonde, match.out=rr, nboots=10, nmc=10)

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